https://doi.org/10.1140/epjp/s13360-023-04542-9
Regular Article
Consequences of Allee effect on the multiple limit cycles in a predator–prey model
1
Department of Applied Mathematics, University of Calcutta, 700009, Kolkata, India
2
Bennett University, 201310, Greater Noida, Uttar Pradesh, India
3
Department of Mathematics, West Bengal State University, West Bengal, India
4
Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Via Marzolo, 8 - 35131 Padova, Italy
Received:
30
July
2023
Accepted:
30
September
2023
Published online:
16
October
2023
In the present paper, we examine the effects of the Allee threshold on prey–predator interaction frameworks developed by utilising the Holling type-III response. Initially, we find the system’s equilibrium and its local stability. According to our analysis, the system follows a transcritical bifurcation about the conversion rate and the saddle node, yet also Hopf bifurcation concerning the Allee factor. In the context of variations in the carrying capacity, Allee threshold and rate of consumption, numerically we investigate the system’s stability scenario and bifurcation layout in the presence of numerous coexistence equilibria. The system exhibits a bistability as well as monostable nature as the Allee parameter progressively increases and three limit cycles arise for lesser and higher intensity of the Allee threshold in which an unstable limit cycle separates two stable limit cycles, as their basin. Depending on the value of the Allee threshold, the population either achieves a stable steady state or oscillates. Numerically, we notice that the system experiences fascinating dynamics followed by transcritical, saddle node and Hopf bifurcation and finally depicts the bistability scenario for various strengths of consumption rates.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
